Space-time coding method using a partitioned position modulation alphabet

ABSTRACT

The invention relates to a space-time coding method for a MIMO-UWB system with P antennas using information symbols belonging to an M-PPM, where M is a multiple of P. The modulation alphabet is partitioned into P sub-alphabets corresponding to successive ranges of modulation positions. An extension of the initial alphabet is obtained by forcing the information symbols to belong to some sub-alphabets, thereby increasing the binary rate of said system.

TECHNICAL DOMAIN

This invention relates to the domain of Ultra Wide Band (UWB)telecommunications and also multi-antenna Space Time Coding (STC)systems.

STATE OF PRIOR ART

Multi-antenna type systems are well known in the state of the art. Thesesystems use a plurality of emission and/or reception antennas and arecalled MIMO (Multiple Input Multiple Output), MISO (Multiple InputSingle Output) or SIMO (Single Input Multiple Output) depending on theadopted configuration type. In the remainder of this description, wewill use the term MIMO to cover the MIMO and MISO variants mentionedabove. Use of spatial diversity on emission and/or on reception enablesthese systems to offer significantly better channel capacities thanclassical single antenna systems (or SISO for Single Input SingleOutput). This spatial diversity is usually completed by temporaldiversity using Space-Time Coding (STC). In this type of coding system,there is one information symbol to be transmitted coded on severalantennas and several transmission instants.

Two large categories of MIMO space time coding category systems areknown: firstly there are Space Time Trellis Coding (STTC) systems, andsecondly Space Time Block Coding (STBC) systems. In a block codingsystem, a block of information symbols to be transmitted is coded into amatrix of transmission symbols, in which one dimension of the matrixcorresponds to the number of antennas and the other corresponds toconsecutive transmission instants.

FIG. 1 diagrammatically shows a MIMO transmission system 100 using STBCcoding. An information symbol block S=(σ₁, . . . ,σ_(b)), for example abinary word containing b bits or more generally b M-ary symbols, iscoded as a space-time matrix:

$\begin{matrix}{C = \begin{pmatrix}c_{1,1} & c_{1,2} & \ldots & c_{1,P} \\c_{2,1} & c_{2,2} & \ldots & c_{2,P} \\\vdots & \vdots & ⋰ & \vdots \\c_{T,1} & c_{T,2} & \ldots & c_{T,P}\end{pmatrix}} & (1)\end{matrix}$

where the coefficients c_(t,p), t=1, . . . ,T; p=1, . . . ,P of the codeare usually complex coefficients dependent on information symbols, P isthe number of antennas used in emission, T is an integer indicating thetime extension of the code, in other words the number of channel uses orPCUs (Per Channel Use).

The function ƒ, that makes the space-time C code word correspond toevery vector S of information symbols, is called the coding function. Ifthe function ƒ is linear, it is said that the space-time code is linear.If the coefficients c_(t,p) are real, the space-time code is said to bereal.

In FIG. 1, a space-time encoder is denoted by 110. At each instant atwhich the channel t is used, the encoder supplies the t-th row vector ofthe matrix C to the multiplexer 120. The multiplexer transmits the rowvector coefficients to the modulators 130 ₁, . . . ,130 _(P), and themodulated signals are transmitted by the antennas 140 ₁, . . . ,140_(P).

The space-time code is characterized by its rate, in other words by thenumber of information symbols that it transmits per instant of channeluse (PCU). The code is said to be full rate if it is P times higher thanthe rate for a single antenna use (SISO).

The space-time code is also characterised by its diversity, that can bedefined as the rank of matrix C. Maximum diversity would occur if thematrix C₁-C₂ is full rank for two arbitrary code words C₁ and C₂corresponding to two vectors S₁ and S₂.

Finally, the space-time code is characterized by its coding gain thattranslates the minimum distance between different code words. It can bedefined as follows:

$\begin{matrix}{\min\limits_{C_{1} \neq C_{2}}{\det \left( {\left( {C_{1} - C_{2}} \right)^{H}\left( {C_{1} - C_{2}} \right)} \right)}} & (2)\end{matrix}$

or equivalently for a linear code:

$\begin{matrix}{\min\limits_{C \neq 0}{\det \left( {C^{H}C} \right)}} & (3)\end{matrix}$

where det(C) refers to the determinant of C and C^(H) is the transposedconjugate matrix of C. The coding gain for transmission energy perinformation symbol is bounded.

A space-time code will be particularly resistant to fading if its codinggain is high.

A first example of space-time coding for a MIMO system with twotransmission antennas was proposed in the article by S. M. Alamoutientitled “A transmit diversity technique for wireless communications”,published in the IEEE Journal on selected areas in communications, vol.16, pp. 1451-1458, October 1998. The Alamouti code is defined by the 2×2space-time matrix:

$\begin{matrix}{C = \begin{pmatrix}\sigma_{1} & \sigma_{2} \\{- \sigma_{2}^{*}} & \sigma_{1}^{*}\end{pmatrix}} & (4)\end{matrix}$

where σ₁ and σ₂ are two information symbols to be transmitted and σ*₁and σ*₂ are their conjugates. As can be seen in the expression (4), thiscode transmits two information symbols for two channel uses andtherefore its rate is one symbol/PCU.

Although initially presented in the above-mentioned article for symbolsbelonging to a QAM modulation, the Alamouti code is also applicable toinformation symbols belonging to a PAM or PSK modulation. On the otherhand, it cannot easily be extended to a Pulse Position Modulation PPM.The symbol in a PPM modulation alphabet with M positions can berepresented by a vector of M components, all null except one that isequal to 1, corresponding to the modulation position at which a pulse isemitted. The use of PPM symbols in the expression (4) then leads to aspace-time matrix with size 2M×2. The term −σ*₂ appearing in the matrixis not a PPM symbol and requires the transmission of a pulse with a signchange. In other words, it is equivalent to using signed PPM symbolsbelonging to an extension of the PPM modulation alphabet.

A second example of a space-time code was proposed in the article by C.Abou-Rjeily et al. entitled “A space-time coded MIMO TH-UWB transceiverwith binary pulse position modulation” published in IEEE CommunicationsLetters, Vol. 11, No. 6, June 2007, pages 522-524. This code isapplicable to multi-antenna systems with a number of transmissionantennas equal to a power of 2, in other words P=2^(p) and toinformation symbols belonging to a Binary Pulse Position Modulation(BPPM) alphabet. More precisely, the proposed space-time code matrix iswritten in the following form:

$\begin{matrix}{C = \begin{pmatrix}\sigma_{1} & \sigma_{2} & \ldots & \sigma_{P} \\{\Omega \; \sigma_{P}} & \sigma_{1} & ⋰ & \vdots \\\vdots & ⋰ & ⋰ & \sigma_{2} \\{\Omega \; \sigma_{2}} & \ldots & {\Omega \; \sigma_{P}} & \sigma_{1}\end{pmatrix}} & (5)\end{matrix}$

in which the BPPM information symbols σ₁,σ₂, . . . ,σ_(P) arerepresented in the form of vectors (1 0)^(T) or (0 1)^(T), the firstvector corresponding to the first PPM position and the second vectorcorresponding to the second PPM position, and where Ω is the 2×2 sizepermutation matrix. This space-time code has the advantage that it doesnot use complex or signed symbols and it has maximum diversity. On theother hand, this code can only transmit one BPPM symbol per channel use(therefore 1 bit/CPU), which is the same as that of a conventionalsingle-antenna system.

A third example of a space-time code was given in the article by C.Abou-Rjeily et al. entitled “A rate-1 2×2 space-time code without anyconstellation extension for TH-UWB communications system with PPM”published in Proceedings of the 2007 VTC Conference, pages 1683-1687,April 2007. This code is applicable to systems with P=2 transmissionantennas and to information symbols belonging to an M-PPM modulationalphabet. More precisely, the matrix of the proposed space-time code iswritten in the form:

$\begin{matrix}{C = \begin{pmatrix}\sigma_{1} & \sigma_{2} \\{\Omega \; \sigma_{2}} & \sigma_{1}\end{pmatrix}} & (6)\end{matrix}$

where the information symbols M-PPM σ₁,σ₂, . . . ,σ_(P) may berepresented in the form of vectors with dimension M, in which M−1components are null and the remaining component equal to 1 indicates themodulation position of the PPM symbol, and where Ω is the permutationmatrix with size M×M.

As in the second example, this space-time code has the advantage that itdoes not use complex or signed symbols. It also has maximum diversityfor all values of M≧2. On the other hand, once again, the code can onlybe used to transmit one M-PPM symbol per channel use (therefore a binaryrate of log₂(M)/PCU) which is the same as for a conventionalsingle-antenna system.

MIMO symbols with space-time coding using UWB (Ultra Wide Band)transmission signals have been proposed in the literature. A UWB signalis a signal conforming with the spectral mask stipulated in the Feb. 14,2002 FCC regulation, revised in March 2005, in other words essentially asignal in the 3.1 to 10.6 GHz spectral band with a band width equal toat least 500 MHz at −10 dB.

UWB signals are divided into two categories: OFDM multi-band signals(MB-OFDM) and UWB pulse type signals. The remainder of this applicationwill only consider pulse type signals.

A pulse UWB signal is composed of very short pulses, typically of theorder of a few hundred picoseconds, distributed within a frame. Adistinct Time Hopping (TH) code is assigned to each user, in order toreduce Multiple Access Interference (MAI). The TH-UWB signal output fromor sent to a user k can then be written in the following form:

$\begin{matrix}{{s_{k}(t)} = {\sum\limits_{n = 0}^{N_{s} - 1}{w\left( {t - {nT}_{s} - {{c_{k}(n)}T_{c}}} \right)}}} & (7)\end{matrix}$

where w is the shape of the elementary pulse, T_(c) is a chip duration,T_(s) is the duration of an elementary interval in whichN_(s)=N_(c)T_(c) where N_(c) is the number of chips in an interval, thetotal frame duration being T_(f)=N_(s)T_(s) where N_(s) is the number ofintervals in the frame. The duration of the elementary pulse is chosento be less than the chip duration, namely T_(w)≦T_(c). The sequencec_(k)(n) for n=0, . . . ,N_(s)−1 defines the time hopping code of theuser k. Time hopping sequences are chosen to minimize the number ofcollisions between pulses belonging to time hopping sequences ofdifferent users.

FIG. 2 shows a TH-UWB signal associated with a user k. It will benoticed that the sequence c_(k)(n), n=0, . . . ,N_(s)−1, for the user inquestion is c_(k)(n)=7,1,4,7 in this case.

In a MIMO system with space-time coding using UWB signals, also calledMIMO-UWB, each antenna transmits a modulated UWB signal as a function ofan information symbol or a block of such symbols. For example, for agiven antenna p, if the information symbols are of the QAM or BPSK type,the signal s^(p)(t) transmitted by this antenna can be expressed keepingthe same notations as above but by ignoring the index for the user:

$\begin{matrix}{{s^{p}(t)} = {\sum\limits_{n = 0}^{N_{s} - 1}{\sigma_{p}{w\left( {t - {nT}_{s} - {{c(n)}T_{c}}} \right)}}}} & (8)\end{matrix}$

where σ_(p) is the transmitted QAM or BPSK information symbol.

Considering the very large band width of UWB signals, it is verydifficult to retrieve phase information at the receiver and therefore todetect an information symbol σ_(p). Furthermore, some UWB systems areunsuitable or hardly suitable for the transmission of signed pulses. Forexample, optical UWB systems only transmit TH-UWB light intensitysignals, which necessarily do not have any sign information.

Space-time codes using PPM symbols avoid the use of complex or signedpulses. If σ_(p) is an M-PPM symbol transmitted by antenna p, the signaltransmitted by this antenna can be expressed in the following form:

$\begin{matrix}{{s^{p}(t)} = {\sum\limits_{n = 0}^{N_{s} - 1}{w\left( {t - {nT}_{s} - {{c(n)}T_{c}} - {\mu_{p}ɛ}} \right)}}} & (9)\end{matrix}$

where ε is a modulation delay (dither) significantly less than the chipduration and μ_(p) ∈{0, . . . ,M−1} is the M-ary PPM position of thesymbol, the first position in this case being considered as introducinga zero delay.

For example, the second and third examples of a space-time codementioned above are well adapted to UWB MIMO systems. However, asmentioned above, these codes cannot give a higher rate than aconventional mono-antenna system.

The purpose of this invention is to propose a space-time coding methodfor a UWB-MIMO system that, although it does not use complex or signedinformation symbols, is capable of reaching higher rates than a singleantenna system.

PRESENTATION OF THE INVENTION

According to a first embodiment, this invention is defined by aspace-time coding method for a UWB transmission system comprising tworadiative elements, said method coding a block of information symbolsS=(σ₁,σ₂,σ₃,σ₄) belonging to a PPM modulation alphabet with an evennumber M of modulation positions, said alphabet being partitioned intofirst and second sub-alphabets corresponding to successive ranges ofmodulation positions, the symbols σ₁,σ₃ belonging to the firstsub-alphabet and the symbols σ₂,σ₄ belonging to the second sub-alphabet,the method coding said symbol block into a sequence of vectors, eachvector being associated with a given use of the transmission channel anda given radiative element, the components of a vector being intended tomodulate the position of a pulse UWB signal, each componentcorresponding to a PPM modulation position, said vectors being obtainedfrom elements of the matrix:

$C = \begin{pmatrix}{\sigma_{1} + \sigma_{2}} & {\sigma_{3} + \sigma_{4}} \\{\Delta \left( {\sigma_{3} + {\Omega \; \sigma_{4}}} \right)} & {\sigma_{1} + {\Omega \; \sigma_{2}}}\end{pmatrix}$

one line of the matrix corresponding to one use of the transmissionchannel and one column of the matrix corresponding to one radiativeelement, the matrix C being defined within one permutation of its rowsand/or its columns, Δ being a permutation of the PPM positions of saidalphabet and Ω being a permutation of the PPM modulation positions ofsaid second sub-alphabet.

The matrix Ω is advantageously a circular permutation, for example acircular shift of said PPM modulation positions of said second alphabet.

According to a second embodiment, the invention is defined by aspace-time coding method for a UWB transmission system comprising threeradiative elements, said method coding a block of information symbolsS=(σ₁,σ₂,σ₃,σ₄,σ₅,σ₆,σ₇,σ₈,σ₉) belonging to a PPM modulation alphabetwith a number M of modulation positions that is a multiple of 3, saidalphabet being partitioned into first, second and third sub-alphabetscorresponding to successive ranges of modulation positions, the σ₁,σ₄,σ₇symbols belonging to the first sub-alphabet, the σ₂,σ₅,σ₈ symbolsbelonging to the second sub-alphabet and the σ₃,σ₆,σ₉ symbols belongingto the third sub-alphabet, the method coding said block of symbols intoa sequence of vectors, each vector being associated with a given use ofthe transmission channel and a given radiative element, components of avector being designed to modulate the position of a pulse UWB signal,each component corresponding to a PPM modulation position, said vectorsbeing obtained from elements of the matrix:

$C = \begin{pmatrix}{\sigma_{1} + \sigma_{2} + \sigma_{3}} & {\sigma_{4} + \sigma_{5} + \sigma_{6}} & {\sigma_{7} + \sigma_{8} + \sigma_{9}} \\{\Delta \left( {\sigma_{7} + {\Omega^{(1)}\sigma_{8}} + \sigma_{9}} \right)} & {\sigma_{1} + {{\Omega \;}^{(1)}\sigma_{2}} + \sigma_{3}} & {\sigma_{4} + {\Omega^{(1)}\sigma_{5}} + \sigma_{6}} \\{\Delta \left( {\sigma_{4} + \sigma_{5} + {\Omega^{(2)}\sigma_{6}}} \right)} & {\Delta \left( {\sigma_{7} + \sigma_{8} + {\Omega^{(2)}\sigma_{9}}} \right)} & {\sigma_{1} + \sigma_{2} + {\Omega^{(2)}\sigma_{3}}}\end{pmatrix}$

one row of the matrix corresponding to one use of the transmissionchannel and one column of the matrix corresponding to one radiativeelement, the matrix C being defined within one permutation of its rowsand/or its columns, Δ being a permutation of the PPM positions of saidalphabet, Ω⁽¹⁾ being a permutation of the PPM modulation positions ofsaid second sub-alphabet and Ω⁽²⁾ being a permutation of the PPMmodulation positions of said third sub-alphabet.

The Ω⁽¹⁾ and/or Ω⁽²⁾ matrices is/are one or more circular permutations,for example one or more circular shifts of the PPM modulation positionsof the second and third sub-alphabets respectively.

According to a third embodiment, the invention is defined by aspace-time coding method for a UWB transmission system comprising aplurality P of radiative elements, said method coding a block ofinformation symbols S=(σ₁,σ₂, . . . ,σ_(P) ₂ ) belonging to a PPMmodulation alphabet with a number M of modulation positions that is amultiple of P, said alphabet being partitioned into P sub-alphabetscorresponding to successive ranges of modulation positions, theσ_(qP+1), q=0, . . . ,P−1 symbols belonging to the first sub-alphabet,the σ_(qP+2), q=0, . . . ,P−1 symbols belonging to the secondsub-alphabet and so on, the σ_(qP+P), q=0, . . . ,P−1 symbols belongingto the Pth sub-alphabet, the method coding said block of symbols into asequence of vectors, each vector being associated with a given use ofthe transmission channel and a given radiative element, the componentsof a vector being intended to modulate the position of a pulse UWBsignal, each component corresponding to a PPM modulation position, saidvectors being obtained from elements of the matrix given in theappendix, one row of the matrix corresponding to one use of thetransmission channel and one column of the matrix corresponding to oneradiative element, the matrix C being defined within one permutation ofits rows and/or its columns, Δ being a permutation of the PPM positionsof said alphabet, the matrices Ω^((p)), p=1, . . . ,P−1 being apermutation of the PPM modulation positions of the (p+1)th sub-alphabet.

At least one matrix Ω^((p)), p=1, . . . ,P−1 may be a circularpermutation, for example a circular shift of the PPM modulationpositions of the (p+1)th sub-alphabet.

In the same way, the matrix Δ may be a circular permutation, for examplea circular shift of said alphabet.

According to a first variant, the radiative elements are UWB antennas.

According to a second variant, the radiative elements are laser diodesor light emitting diodes.

Advantageously, said pulse signal may be a TH-UWB signal.

BRIEF DESCRIPTION OF THE DRAWINGS

Other characteristics and advantages of the invention will become clearafter reading a preferred embodiment of the invention with reference tothe appended figures among which:

FIG. 1 diagrammatically shows a known MIMO transmission system with STBCcoding according to the state of the art;

FIG. 2 shows the shape of a TH-UWB signal;

FIG. 3 diagrammatically shows a multi-antenna UWB transmission systemaccording to a first embodiment of the invention;

FIG. 4 diagrammatically shows a multi-antenna UWB transmission systemaccording to a second embodiment of the invention.

DETAILED PRESENTATION OF PARTICULAR EMBODIMENTS

The basic idea of this invention is to partition a PPM modulationalphabet into distinct ranges and to create an extension of the PPMmodulation alphabet starting from the alphabet that was thuspartitioned, the space-time code being generated from a block of symbolsbelonging to the alphabet thus extended. As we will see later, theextension of the alphabet can increase the rate of the code.

According to a first embodiment, we will firstly assume a UWBtransmission system with P=2 transmission antennas or more generallywith P=2 radiative elements.

We will also assume that we have an M-PPM modulation alphabet denoted A,with an even number M of modulation positions. These positions may bearranged in a given time order, for example {1, . . . ,M}, where 1 isthe minimum time shift and M is the maximum time shift. In the remainderof this description, a modulation position will indifferently berepresented by an index m ∈ {1, . . . ,M} or by a vector σ with size Mand components that are all zero except for the mth component equal to1, defining the position concerned.

The alphabet A is partitioned in two separate consecutive ranges, orsub-alphabets, namely

$A_{1} = \left\{ {1,\ldots \mspace{14mu},\frac{M}{2}} \right\}$

and

$A_{2} = {\left\{ {{\frac{M}{2} + 1},M} \right\}.}$

We will consider blocks of information symbols S=(σ₁,σ₂,σ₃,σ₄) in whichσ₁,σ₂,σ₃,σ₄ are symbols of A such that σ₁,σ₃ ∈ A₁ and σ₂,σ₄ ∈ A₂. Thealphabet Ã composed of quadruples σ₁,σ₂,σ₃,σ₄ satisfies the abovecondition, namely:

Ã={(σ₁,σ₂,σ₃,σ₄)|σ₁,σ₃ ∈ A ₁ et σ ₂,σ₄ ∈ A ₂}  (10)

is an extension of the alphabet A, with cardinal

${{{Card}\left( \overset{\sim}{A} \right)} = \left( \frac{M}{2} \right)^{4}},$

since

${{Card}\left( A_{1} \right)} = {{{Card}\left( A_{2} \right)} = {\frac{M}{2}.}}$

For example for an 8-PPM alphabet, the alphabet Ã will be composed ofquadruples σ₁,σ₂,σ₃,σ₄, such as:

$\sigma_{1},{\sigma_{3} \in \left\{ {\begin{pmatrix}1 \\0 \\0 \\0 \\0 \\0 \\0 \\0\end{pmatrix},\begin{pmatrix}0 \\1 \\0 \\0 \\0 \\0 \\0 \\0\end{pmatrix},\begin{pmatrix}0 \\0 \\1 \\0 \\0 \\0 \\0 \\0\end{pmatrix},\begin{pmatrix}0 \\0 \\0 \\1 \\0 \\0 \\0 \\0\end{pmatrix}} \right\}}$ and$\sigma_{2},{\sigma_{4} \in \left\{ {\begin{pmatrix}0 \\0 \\0 \\0 \\1 \\0 \\0 \\0\end{pmatrix},\begin{pmatrix}0 \\0 \\0 \\0 \\0 \\1 \\0 \\0\end{pmatrix},\begin{pmatrix}0 \\0 \\0 \\0 \\0 \\0 \\1 \\0\end{pmatrix},\begin{pmatrix}0 \\0 \\0 \\0 \\0 \\0 \\0 \\1\end{pmatrix}} \right\}}$

In the general case of an M-PPM alphabet in which M is even, thespace-time code used by the MIMO-UWB system with two antennas is definedby the following matrix with size 2M×2:

$\begin{matrix}{C = \begin{pmatrix}{\sigma_{1} + \sigma_{2}} & {\sigma_{3} + \sigma_{4}} \\{\Delta \left( {\sigma_{3} + {\Omega\sigma}_{4}} \right)} & {\sigma_{1} + {\Omega\sigma}_{2}}\end{pmatrix}} & (11)\end{matrix}$

where σ₁,σ₂,σ₃,σ₄ are information symbols to be transmitted, representedin the form of column vectors with size M;Ω is a matrix with size M×M defined by:

$\begin{matrix}{\Omega = \begin{pmatrix}I_{M^{\prime}} & 0_{M^{\prime}} \\0_{M^{\prime}} & \Omega^{\prime}\end{pmatrix}} & (12)\end{matrix}$

where

${M^{\prime} = \frac{M}{2}},$

in which I_(M′) and 0_(M′) are the unit matrix and the zero matrix withsize M′×M′ respectively, and Ω′ is a permutation matrix with size M′×M′.It will be noted that the matrix Ω will only permute the modulationpositions of the alphabet A₂;Δ is a permutation matrix with size M×M operating on modulationpositions of the alphabet A.

A permutation on a set of modulation positions is any bijection of thisset on itself, except for the unit matrix we have unit. The permutationmatrix Ω′ may in particular be a circular permutation matrix on the lastM′ positions, for example a simple circular shift:

$\begin{matrix}\begin{matrix}{\Omega^{\prime} = \begin{pmatrix}0_{{1 \times M^{\prime}} - 1} & 1 \\I_{M^{\prime} - {1 \times M^{\prime}} - 1} & 0_{M^{\prime} - {1 \times 1}}\end{pmatrix}} \\{= \begin{pmatrix}0 & 0 & \ldots & 0 & 1 \\1 & 0 & \ldots & 0 & 0 \\0 & 1 & 0 & ⋰ & \vdots \\\vdots & ⋰ & ⋰ & ⋰ & 0 \\0 & \ldots & 0 & 1 & 0\end{pmatrix}}\end{matrix} & (13)\end{matrix}$

where I_(M′−1×M′−1) is the unit matrix with size M′−1 , 0_(1×M′″1) isthe null row vector with size M′−1, 0_(M′−1×1) is the null column vectorwith size M′″1.

Similarly, the matrix Δ may be a circular permutation on the Mmodulation positions of the alphabet A, for example a simple circularshift:

$\begin{matrix}\begin{matrix}{\Delta = \begin{pmatrix}0_{{1 \times M} - 1} & 1 \\I_{M - {1 \times M} - 1} & 0_{M - {1 \times 1}}\end{pmatrix}} \\{= \begin{pmatrix}0 & 0 & \ldots & 0 & 1 \\1 & 0 & \ldots & 0 & 0 \\0 & 1 & 0 & ⋰ & \vdots \\\vdots & ⋰ & ⋰ & ⋰ & 0 \\0 & \ldots & 0 & 1 & 0\end{pmatrix}}\end{matrix} & (14)\end{matrix}$

where I_(M−1×M−1) is the unit matrix with size M−1, 0_(1×M−1) is thenull row vector with size M−1, 0_(M−1×1) is the null column vector withsize M−1.

It is important to note that the space-time code is defined within onepermutation of the rows and columns of C. A permutation on the rows—inthis description a row is a row of vectors in the expression (11)—and/orthe columns of C is also a space-time code according to the invention, apermutation on the rows being equivalent to one permutation of thechannel use instants and a permutation on the columns being equivalentto a permutation of the transmission antennas.

As can be seen from (11), components of the matrix C are simply 0s and1s and not signed values. Consequently, these components do notintroduce any phase inversion nor generally a phase shift. Thisspace-time code is equally suitable for modulation of an ultra-wide bandsignal.

Furthermore, the matrix C has the same number of “1s” in each of itscolumns (four “1” values, namely two “1” values per PCU), which resultsin a beneficial equal distribution of energy on the different antennas.

We can explicitly describe the space-time code matrix in the case inwhich the Ω′ and Δ matrices are the matrices given by expressions (13)and (14) respectively:

$\begin{matrix}{C = \begin{pmatrix}\sigma_{1,1} & \sigma_{3,1} \\\sigma_{1,2} & \sigma_{3,2} \\\vdots & \vdots \\\sigma_{1,M^{\prime}} & \sigma_{3,M^{\prime}} \\\sigma_{2,{M^{\prime} + 1}} & \sigma_{4,{M^{\prime} + 1}} \\\sigma_{2,{M^{\prime} + 2}} & \sigma_{4,{M^{\prime} + 2}} \\\vdots & \vdots \\\sigma_{2,M} & \sigma_{4,M} \\\sigma_{4,{M - 1}} & \sigma_{1,1} \\\sigma_{3,1} & \sigma_{1,2} \\\vdots & \vdots \\\sigma_{3,M^{\prime}} & \sigma_{1,M^{\prime}} \\\sigma_{4,M} & \sigma_{2,M} \\\sigma_{4,1} & \sigma_{2,1} \\\vdots & \vdots \\\sigma_{4,{M - 2}} & \sigma_{2,{M - 1}}\end{pmatrix}} & (15)\end{matrix}$

where σ_(i)=(σ_(i1),σ_(i2), . . .,σ_(iM))^(T) for i=1, . . . ,4. Theexpression (15) is obtained taking account of the fact that the last Mcomponents of σ₁,σ₃ and the first M components of σ₂,σ₄ are null.

It will be noted that the binary rate of the space-time code defined byexpression (11) is:

$\begin{matrix}{R = {\frac{\log_{2}\left( \left( \frac{M}{2} \right)^{4} \right)}{2} = {2{\log_{2}\left( \frac{M}{2} \right)}}}} & (16)\end{matrix}$

For example, for an 8-PPM modulation, the rate will be 4 bits/CPU whilethe rate of a conventional single-antenna system is 3 bits/CPU. The gainin rate will be particularly marked if the order of the PPM modulationis higher.

Furthermore, it can be shown that the space-time code has maximumdiversity. It will be remembered that a code is maximum diversity ifΔC=C−C′ is full rank for any pair of distinct matrices C,C′ of the code.If the ΔC matrix is not full rank, this would mean that its two columnvectors:

$\begin{matrix}{{\Delta \; C} = \begin{pmatrix}{{\delta \; \sigma_{1}} + {\delta \; \sigma_{2}}} & {{\delta \; \sigma_{3}} + {\delta \; \sigma_{4}}} \\{\Delta \left( {{\delta \; \sigma_{3}} + {\Omega \; \delta \; \sigma_{4}}} \right)} & {{\delta \; \sigma_{1}} + {\Omega \; \delta \; \sigma_{2}}}\end{pmatrix}} & (17)\end{matrix}$

where δσ_(i)=σ_(i)−σ′_(i), would be co-linear. The first line ΔC clearlyshows that this means that δσ₁=δσ₃ and δσ₂=δσ₄ and the second lineclearly shows that δσ₁=δσ₃=δσ₂=δσ₄=0, in other words ΔC=0.

FIG. 3 shows an example of a UWB transmission system with two radiativeelements, according to a first embodiment of the invention. Theradiative elements may be UWB antennas, laser diodes or infrared LEDs.The system 300 comprises a space-time encoder 320, two UWB modulatorsdenoted by 331 and 332 and two UWB antennas 341 and 342. The encoder 320receives blocks of information symbols S=(σ₁,σ₂,σ₃,σ₄) belonging to thealphabet Ã and calculates the elements of the matrix C satisfying theexpression (11) or a variant obtained by permutation of its rows and/orcolumns as mentioned above. In the case of a space-time code defined by(11), the encoder 320 transmits the vectors σ₁+σ₂ and σ₃+σ₄ tomodulators 331 and 332 respectively during the first channel use, andvectors Δ(σ₃+Ωσ₄) and σ₁+Ωσ₂ during the second channel use.

The UWB modulator 331 generates the corresponding modulated pulse UWBsignals from the column vectors σ₁+σ₂ and Δ(σ₃+Ωσ₄), and transmits themto the radiative element 341 during the first and second channel uses,respectively. Similarly, the UWB modulator 332 starts from the vectorsσ₃+σ₄ and σ₁+Ωσ₂ and generates the corresponding modulated pulse UWBsignals and transmits them to the radiative element 342 during the firstand second channel uses respectively.

The system 300 may also comprise a transcoder 310 adapted to receivinginformation symbols, for example binary symbols A=(a₁,a₂, . . . ,a_(b)),and coding them in the form of blocks S ∈ Ã. The transcoder may alsocomprise source coding means and/or channel coding means before thetranscoding operation itself, in a manner known as such.

For example, we can describe the signals transmitted by the antennas 341and 342 during the two transmission instants when the space-time code isdefined by the expression (15). It is also assumed that the modulators331, 332 do a TH-UWB type modulation.

During the first channel use, the antenna 341 transmits a first frame,namely by using the notations in (9):

$\begin{matrix}\begin{matrix}{{s^{1}(t)} = {\sum\limits_{n = 0}^{N_{s} - 1}{\sum\limits_{m = 1}^{M}{\left( {\sigma_{1,m} + \sigma_{2,m}} \right){w\left( {t - {nT}_{s} - {{c(n)}T_{c}} - {m\; ɛ}} \right)}}}}} \\{= {{\sum\limits_{n = 0}^{N_{s} - 1}{w\left( {t - {nT}_{s} - {{c(n)}T_{c}} - {\mu_{1}ɛ}} \right)}} +}} \\{{w\left( {t - {nT}_{s} - {{c(n)}T_{c}} - {\mu_{2}ɛ}} \right)}}\end{matrix} & (18)\end{matrix}$

where μ₁ and μ₂ are the corresponding modulation positions of the σ₁ andσ₂ symbols, where 1≦μ₁≦M′ and M′+1≦μ₂≦M. The first PPM position in thiscase corresponds to a time shift of ε but a zero shift could alternatelyhave been envisaged.

At the same time, the antenna 342 transmits a first frame:

$\begin{matrix}\begin{matrix}{{s^{2}(t)} = {\sum\limits_{n = 0}^{N_{s} - 1}{\sum\limits_{m = 1}^{M}{\left( {\sigma_{3,m} + \sigma_{4,m}} \right){w\left( {t - {nT}_{s} - {{c(n)}T_{c}} - {mɛ}} \right)}}}}} \\{= {{\sum\limits_{n = 0}^{N_{s} - 1}{w\left( {t - {nT}_{s} - {{c(n)}T_{c}} - {\mu_{3}ɛ}} \right)}} +}} \\{{w\left( {t - {nT}_{s} - {{c(n)}T_{c}} - {\mu_{4}ɛ}} \right)}}\end{matrix} & (19)\end{matrix}$

During the second use of the channel, the antenna 341 transmits a secondframe:

$\begin{matrix}\begin{matrix}{{s^{2}(t)} = {\sum\limits_{n = 0}^{N_{s} - 1}{\sum\limits_{m = 1}^{M}{\left( {\sigma_{3,{\omega {(m)}}} + \sigma_{4,{\delta \cdot {\omega {(m)}}}}} \right){w\left( {t - {nT}_{s} - {{c(n)}T_{c}} - {m\; ɛ}} \right)}}}}} \\{= {{\sum\limits_{n = 0}^{N_{s} - 1}{w\left( {t - {nT}_{s} - {{c(n)}T_{c}} - {{\omega \left( \mu_{3} \right)}ɛ}} \right)}} +}} \\{{w\left( {t - {nT}_{s} - {{c(n)}T_{c}} - {{\delta \cdot {\omega \left( \mu_{4} \right)}}ɛ}} \right)}}\end{matrix} & (20)\end{matrix}$

where ω(.) is the straight circular shift of {M′+1, . . . ,M}corresponding to Ω and δ(.) is the straight circular shift on {1,2, . .. ,M} corresponding to Δ and ∘ is the composition operation.And the antenna 342 simultaneously transmits a second frame:

$\begin{matrix}\begin{matrix}{{s^{2}(t)} = {\sum\limits_{n = 0}^{N_{s} - 1}{\sum\limits_{m = 1}^{M}{\left( {\sigma_{1,m} + \sigma_{2,{\omega {(m)}}}} \right){w\left( {t - {nT}_{s} - {{c(n)}T_{c}} - {m\; ɛ}} \right)}}}}} \\{= {{\sum\limits_{n = 0}^{N_{s} - 1}{w\left( {t - {nT}_{s} - {{c(n)}T_{c}} - {\mu_{1}ɛ}} \right)}} +}} \\{{w\left( {t - {nT}_{s} - {{c(n)}T_{c}} - {{\omega \left( \mu_{2} \right)}ɛ}} \right)}}\end{matrix} & (21)\end{matrix}$

According to a second embodiment, the MIMO system comprises P=3 UWBantennas and the number M of modulation positions is a multiple of 3.The alphabet A is partitioned into three separate consecutive ranges orsub-alphabets, namely

$A_{1} = \left\{ {1,\ldots \mspace{14mu},\frac{M}{3}} \right\}$

We will consider

$A_{2} = {{\left\{ {{\frac{M}{3} + 1},\frac{2M}{3}} \right\} \mspace{14mu} {and}\mspace{14mu} A_{3}} = {\left\{ {{\frac{2M}{3} + 1},M} \right\}.}}$

blocks of information symbols S=(σ₁,σ₂,σ₃,σ₄,σ₅,σ₆,σ₇,σ₈,σ₉) whereσ₁,σ₂,σ₃,σ₄,σ₅,σ₆,σ₇,σ₈,σ₉ are symbols of A such that σ₁,σ₄,σ₇ ∈ A₁,σ₂,σ₅,σ₈ ∈ A₂ and σ₃,σ₆,σ₉ ∈ A₃. The alphabet Ã is composed of nonupletsσ₁,94 ₂,σ₃,σ₄,σ₅,σ₆,σ₇,σ₈,σ₉ satisfying the previous condition, in otherwords:

Ã={(σ₁,σ₂,σ₃,σ₄,σ₅,σ₆,σ₇,σ₈σ₉)|σ₁,σ₄,σ₇ ∈ A ₁; σ₂,σ₅,σ₈ ∈ A ₂; σ₃,σ₆,σ₉∈ A ₃}  (22)

is an extension of the alphabet A, with cardinal

${{{Card}\mspace{11mu} \left( \overset{\sim}{A} \right)} = \left( \frac{M}{3} \right)^{9}},$

since

$\begin{matrix}{{{Card}\mspace{11mu} \left( A_{1} \right)} = {{Card}\mspace{11mu} \left( A_{2} \right)}} \\{= {{Card}\mspace{11mu} \left( A_{2} \right)}} \\{= {\frac{M}{3}.}}\end{matrix}$

For example for a 6-PPM alphabet, the alphabet Ã will be composed ofnonuplets σ₁,σ₂,σ₃,σ₄,σ₅,σ₆,σ₇,σ₈σ₉, such that:

$\begin{matrix}{{\sigma_{1},\sigma_{4},{{\sigma_{7} \in \left\{ {\begin{pmatrix}1 \\0 \\0 \\0 \\0 \\0\end{pmatrix},\begin{pmatrix}0 \\1 \\0 \\0 \\0 \\0\end{pmatrix}} \right\}};}}{\sigma_{2},\sigma_{5},{{\sigma_{8} \in \left\{ {\begin{pmatrix}0 \\0 \\1 \\0 \\0 \\0\end{pmatrix},\begin{pmatrix}0 \\0 \\0 \\1 \\0 \\0\end{pmatrix}} \right\}};}}{\sigma_{3},\sigma_{6},{{\sigma_{9} \in \left\{ {\begin{pmatrix}0 \\0 \\0 \\0 \\1 \\0\end{pmatrix},\begin{pmatrix}0 \\0 \\0 \\0 \\0 \\1\end{pmatrix}} \right\}};}}} & (23)\end{matrix}$

In the general case of an M-PPM alphabet, where M is a multiple of 3,the space-time code used by the MIMO-UWB system with three antennas isdefined by the following matrix with size 3M×3:

$\begin{matrix}{C = \begin{pmatrix}{\sigma_{1} + \sigma_{2} + \sigma_{3}} & {\sigma_{4} + \sigma_{5} + \sigma_{6}} & {\sigma_{7} + \sigma_{8} + \sigma_{9}} \\{\Delta \left( {\sigma_{7} + {\Omega^{(1)}\sigma_{8}} + \sigma_{9}} \right)} & {\sigma_{1} + {\Omega^{(1)}\sigma_{2}} + \sigma_{3}} & {\sigma_{4} + {\Omega^{(1)}\sigma_{5}} + \sigma_{6}} \\{\Delta \left( {\sigma_{4} + \sigma_{5} + {\Omega^{(2)}\sigma_{6}}} \right)} & {\Delta \left( {\sigma_{7} + \sigma_{8} + {\Omega^{(2)}\sigma_{9}}} \right)} & {\sigma_{1} + \sigma_{2} + {\Omega^{(2)}\sigma_{3}}}\end{pmatrix}} & (24)\end{matrix}$

where σ₁,σ₂,σ₃,σ₄,σ₅,σ₆,σ₇,σ₇,σ₈,σ₉ are information symbols to betransmitted represented in the form of column vectors with size M;Ω⁽¹⁾ is a matrix with size M×M defined by:

$\begin{matrix}{\Omega^{(1)} = \begin{pmatrix}I_{M^{\prime}} & 0_{M^{\prime}} & 0_{M^{\prime}} \\0_{M^{\prime}} & \Omega^{\prime} & 0_{M^{\prime}} \\0_{M^{\prime}} & 0_{M^{\prime}} & I_{M^{\prime}}\end{pmatrix}} & (25)\end{matrix}$

where

${M^{\prime} = \frac{M}{3}},$

where I_(M′) is the unit matrix and 0_(M′) is the null matrix with sizeM′×M′ and Ω′ is a permutation matrix with size M′×M′. Note that the Ω⁽¹⁾matrix will only permute the modulation positions of the alphabet A₂;Ω⁽²⁾ is a matrix with size M×M defined by:

$\begin{matrix}{\Omega^{(2)} = \begin{pmatrix}I_{M^{\prime}} & 0_{M^{\prime}} & 0_{M^{\prime}} \\0_{M^{\prime}} & I_{M^{\prime}} & 0_{M^{\prime}} \\0_{M^{\prime}} & 0_{M^{\prime}} & \Omega^{\prime}\end{pmatrix}} & (26)\end{matrix}$

using the same notation conventions as above. It will be noted that theΩ⁽²⁾ matrix only permutes the modulation positions of the alphabet A₃.

Δ is a permutation matrix with size M×M operating on modulationpositions of the alphabet A.

The matrices Δ and Ω′ may be circular permutation matrices or evensimple circular shift matrices as above. Obviously, the space-time codeis also defined within one permutation of the rows and columns of C.

The binary rate of the space-time code defined by expression (24) is:

$\begin{matrix}\begin{matrix}{R = \frac{\log_{2}\left( \left( \frac{M}{3} \right)^{9} \right)}{3}} \\{= {3\; {\log_{2}\left( \frac{M}{3} \right)}}}\end{matrix} & (27)\end{matrix}$

The space-time code is also maximum diversity and has beneficialproperties already mentioned for the first embodiment.

FIG. 4 shows an example of a UWB transmission system with threeradiative elements according to a second embodiment of the invention.The radiative element may be UWB antennas, laser diodes or infraredLEDs. The system 400 comprises a space-time encoder 420, three UWBmodulators denoted by 431, 432 and 433 and three UWB antennas, 441, 442and 443. The encoder 420 receives blocks of information symbolsS=(σ₁,σ₂,σ₃,σ₄,σ₅,σ₆,σ₇,σ₈,σ₉) belonging to the alphabet Ã andcalculates elements of the matrix C satisfying the expression (24) or avariant obtained by permutation of its rows and/or its columns asdescribed above. In the case of a space-time code defined by (24), theencoder 420 transmits the vectors σ₁+σ₂+σ₃, σ₄+σ₅+σ₆, σ₇+σ₈+σ₉ duringthe first channel use, vectors Δ(σ₇+Ω⁽¹⁾σ₈+σ₉), σ₁+Ω⁽¹⁾σ₂+σ₃ andσ₄+Ω⁽¹⁾σ₅+σ₆ during the second channel use, and finally the vectorsΔ(σ₄+σ₅+Ω⁽²⁾σ₆), Δ(σ₇+σ₈+Ω⁽²⁾σ₉) and σ₁+σ₂+Ω⁽²⁾σ₃ during the thirdchannel use, to modulators 431, 432 and 433 respectively.

The UWB modulator 431 starts from the column vectors σ₁+σ₂+σ₃,Δ(σ₇+Ω⁽¹⁾σ₈+σ₉) and Δ(σ₇+Ω⁽¹⁾σ₈+σ₉) and generates the correspondingmodulated pulse UWB signals and transmits them to the antenna 441 duringthe first, second and third channel uses respectively. Similarly, theUWB modulator 432 starts from the column vectors σ₄+σ₅+σ₆, σ₁+Ω⁽¹⁾σ₂+σ₃et Δ(σ₇+Ω⁽¹⁾σ₈+σ₉) and generates the corresponding modulated pulse UWBsignals and transmits them to the antenna 442 during the first, secondand third channel uses respectively. Finally, the UWB modulator 433starts from the column vectors σ₇+σ₈+σ₉, σ₄+Ω⁽¹⁾σ₅+σ₆ and σ₁+σ₂+Ω⁽²⁾σ₃and generates the corresponding modulated pulse UWB signals andtransmits them to the antenna 443 during the first, second and thirdchannel uses respectively.

Like the first embodiment, the system 400 may comprise a transcoder 410adapted to receive information symbols, for example binary symbolsA=(a₁,a₂, . . . ,a_(b)) and to code them in the form of S ∈ Ã blocks.

More generally, the first and second embodiments may be generalised tothe case of a MIMO-UWB system with P radiative elements for a number ofmodulation positions M that is a multiple P. We set

$M^{\prime} = {\frac{M}{P}.}$

The alphabet A may be partitioned into P separate consecutive ranges orsub-alphabets, namely A₁={1, . . . ,M′}, A₂={M′+1, . . . ,2M′}, . . . ,A_(P)={M−M′+1, . . . ,M}.

We will consider that blocks of information symbols S=(σ₁,σ₂, . . .,σ_(P) ₂ ) in which σ₁,σ₂, . . . ,σ_(P) ₂ are symbols of A such thatσ_(qP+1) ∈A₁, σ_(qP+2) ∈ A₂, . . . , σ_(qP+P) ∈ A_(P) where q=0, . . .,P−1. The alphabet Ã composed of P²-uplets satisfying the previouscondition, in other words:

Ã={(σ₁,σ₂, . . . ,σ_(P) ₂ )|σ_(qP+1) ∈ A ₁; σ_(qP+2), ∈ A ₂; . . .,σ_((q+1)P) ∈ A _(P); q=0, . . . ,P−1}  (28)

is an extension of the alphabet A, with cardinal Card(Ã)=(M′)^(P) ² ,because Card(A_(p))=M′.

The space-time code used by the MIMO-UWB system with P antennas isdefined by the matrix C with size PM×P given in the appendix.

The Ω^((p)), p=1, . . . ,P−1 matrices are size M×M matrices defined by:

$\begin{matrix}{\Omega^{(1)} = \begin{pmatrix}I_{M^{\prime}} & 0_{M^{\prime}} & \ldots & 0_{M^{\prime}} \\0_{M^{\prime}} & \Omega^{\prime} & \ldots & 0_{M^{\prime}} \\\vdots & \vdots & ⋰ & \vdots \\0_{M^{\prime}} & 0_{M^{\prime}} & \ldots & I_{M^{\prime}}\end{pmatrix}} & (29)\end{matrix}$

and so on, the Ω′ matrix occupying successive positions on the diagonaluntil:

$\begin{matrix}{\Omega^{({P - 1})} = \begin{pmatrix}I_{M^{\prime}} & 0_{M^{\prime}} & \ldots & 0_{M^{\prime}} \\0_{M^{\prime}} & I_{M^{\prime}} & \ldots & 0_{M^{\prime}} \\\vdots & \vdots & ⋰ & \vdots \\0_{M^{\prime}} & 0_{M^{\prime}} & \ldots & \Omega^{\prime}\end{pmatrix}} & (30)\end{matrix}$

where I_(M′) is the unit matrix and 0_(M′) is the null matrix with sizeM′×M′, and Ω′ is a permutation matrix with size M′×M′. It will be notedthat matrix Ω^((p)), p=1, . . . ,P−1, only permutes the modulationpositions of the alphabet A_(p+1).Δ is a permutation matrix with size M×M operating on the modulationpositions of the alphabet A.

The space-time code is once again defined within one permutation of therows and columns of C.

In general, the conclusions described for the first embodiment (P=2) andthe second embodiment (P=3) are also valid for P>3. In particular, thebinary rate of the system is:

$\begin{matrix}\begin{matrix}{R = \frac{\log_{2}\left( \left( M^{\prime} \right)^{P^{2}} \right)}{P}} \\{= {P\; {\log_{2}\left( \frac{M}{P} \right)}}}\end{matrix} & (31)\end{matrix}$

which is greater than the rate of a conventional single antenna systemlog₂(M). The space-time code also has maximum diversity properties, withunsigned nature and power balance between antennas.

The UWB signals transmitted by the system illustrated in FIGS. 3, 4 ormore generally by a MIMO-UWB system with P antennas using the space-timeencoder described above may be processed in a conventional manner by amulti-antenna receiver. For example, the receiver can include a Raketype correlation stage followed by a decision stage, for example using asphere decoder known those skilled in the art.

Appendix: $C = \begin{pmatrix}{\sigma_{1} + \sigma_{2} + \ldots + \sigma_{P}} & {\sigma_{P + 1} + \sigma_{P + 2} + \ldots + \sigma_{2P}} & \ldots & {\sigma_{{P{({P - 1})}} + 1} + \sigma_{{P{({P - 1})}} + 2} + \ldots + \sigma_{P^{2}}} \\{\Delta \left( {\sigma_{{P{({P - 1})}} + 1} + {\Omega^{(1)}\sigma_{{P{({P - 1})}} + 2}} + \ldots + \sigma_{P^{2}}} \right)} & {\sigma_{1} + {\Omega^{(1)}\sigma_{2}} + \ldots + \sigma_{P}} & \ldots & {\sigma_{{P{({P - 2})}} + 1} + \sigma_{{P{({P - 2})}} + 2} + \ldots + \sigma_{P{({P - 1})}}} \\\vdots & \vdots & ⋰ & \vdots \\{\Delta \left( {\sigma_{{P{({P - 2})}} + 1} + \sigma_{{P{({P - 2})}} + 2} + \ldots + {\Omega^{(P)}\sigma_{P{({P - 1})}}}} \right)} & {\Delta \left( {\sigma_{{P{({P - 1})}} + 1} + \sigma_{{P{({P - 1})}} + 2} + \ldots + {\Omega^{(P)}\sigma_{P^{2}}}} \right)} & \ldots & {\sigma_{1} + \sigma_{2} + \ldots + {\Omega^{(P)}\sigma_{P}}}\end{pmatrix}$

1. Space-time coding method for a UWB transmission system comprising tworadiative elements, said method coding a block of information symbolsS=(σ₁,σ₂,σ₃,σ₄) belonging to a PPM modulation alphabet with an evennumber M of modulation positions, said alphabet being partitioned intofirst and second sub-alphabets corresponding to successive ranges ofmodulation positions, the symbols σ₁,σ₃ belonging to the firstsub-alphabet and the symbols σ₂,σ₄ belonging to the second sub-alphabet,the method coding said symbol block into a sequence of vectors, eachvector being associated with a given use of the transmission channel anda given radiative element, the components of a vector being intended tomodulate the position of a pulse UWB signal, each componentcorresponding to a PPM modulation position, characterised in that saidvectors are obtained from elements of the matrix: $C = \begin{pmatrix}{\sigma_{1} + \sigma_{2}} & {\sigma_{3} + \sigma_{4}} \\{\Delta \left( {\sigma_{3} + {\Omega\sigma}_{4}} \right)} & {\sigma_{1} + {\Omega\sigma}_{2}}\end{pmatrix}$ one line of the matrix corresponding to one use of thetransmission channel and one column of the matrix corresponding to oneradiative element, the matrix C being defined within one permutation ofits rows and/or its columns, Δ being a permutation of the PPM positionsof said alphabet and Ω being a permutation of the PPM modulationpositions of said second sub-alphabet.
 2. Space-time coding methodaccording to claim 1, characterised in that Ω is a circular permutationof PPM modulation positions of said second sub-alphabet.
 3. Space-timecoding method according to claim 2, characterised in that Ω is acircular shift of PPM modulation positions of said second alphabet. 4.Space-time coding method for a UWB transmission system comprising threeradiative elements, said method coding a block of information symbolsS=(σ₁,σ₂,σ₃,σ₄,σ₅,σ₆,θ₇,σ₈,σ₉) belonging to a PPM modulation alphabetwith a number M of modulation positions that is a multiple of 3, saidalphabet being partitioned into first, second and third sub-alphabetscorresponding to successive ranges of modulation positions, the σ₁,σ₄,σ₇symbols belonging to the first sub-alphabet, the σ₂,σ₅,σ₈ symbolsbelonging to the second sub-alphabet and the σ₃,σ₆,σ₉ symbols belongingto the third sub-alphabet, the method coding said block of symbols intoa sequence of vectors, each vector being associated with a given use ofthe transmission channel and a given radiative element, components of avector being designed to modulate the position of a pulse UWB signal,each component corresponding to a PPM modulation position, characterisedin that said vectors are obtained from elements of the matrix:$C = \begin{pmatrix}{\sigma_{1} + \sigma_{2} + \sigma_{3}} & {\sigma_{4} + \sigma_{5} + \sigma_{6}} & {\sigma_{7} + \sigma_{8} + \sigma_{9}} \\{\Delta \left( {\sigma_{7} + {\Omega^{(1)}\sigma_{8}} + \sigma_{9}} \right)} & {\sigma_{1} + {\Omega^{(1)}\sigma_{2}} + \sigma_{3}} & {\sigma_{4} + {\Omega^{(1)}\sigma_{5}} + \sigma_{6}} \\{\Delta \left( {\sigma_{4} + \sigma_{5} + {\Omega^{(2)}\sigma_{6}}} \right)} & {\Delta \left( {\sigma_{7} + \sigma_{8} + {\Omega^{(2)}\sigma_{9}}} \right)} & {\sigma_{1} + \sigma_{2} + {\Omega^{(2)}\sigma_{3}}}\end{pmatrix}$ one row of the matrix corresponding to one use of thetransmission channel and one column of the matrix corresponding to oneradiative element, the matrix C being defined within one permutation ofits rows and/or its columns, Δ being a permutation of the PPM positionsof said alphabet, Ω⁽¹⁾ being a permutation of the PPM modulationpositions of said second sub-alphabet and Ω⁽²⁾ being a permutation ofthe PPM modulation positions of said third sub-alphabet.
 5. Space-timecoding method according to claim 4, characterised in that Ω⁽¹⁾ and/orΩ⁽²⁾ is/are one or more circular permutations of the PPM modulationpositions of the second and third sub-alphabets respectively. 6.Space-time coding method according to claim 5, characterised in thatΩ⁽¹⁾ and/or Ω⁽²⁾ is/are one or more circular shifts of the PPMmodulation positions of said second and third sub-alphabetsrespectively.
 7. Space-time coding method for a UWB transmission systemcomprising a plurality P of radiative elements, said method coding ablock of information symbols S=(σ₁,σ₂, . . . ,σ_(P) ₂ ) belonging to aPPM modulation alphabet with a number M of modulation positions that isa multiple of P, said alphabet being partitioned into P sub-alphabetscorresponding to successive ranges of modulation positions, theσ_(qP+1), q=0, . . . ,P−1 symbols belonging to the first sub-alphabet,the σ_(qP+2), q=0, . . . ,P−1 symbols belonging to the secondsub-alphabet, and so on, the σ_(qP+P), q=0, . . . ,P−1 symbols belongingto the Pth sub-alphabet, the method coding said block of symbols into asequence of vectors, each vector being associated with a given use ofthe transmission channel and a given radiative element, the componentsof a vector being intended to modulate the position of a pulse UWBsignal, each component corresponding to a PPM modulation position,characterised in that said vectors are obtained from elements of thematrix given in the appendix, one row of the matrix corresponding to oneuse of the transmission channel and one column of the matrixcorresponding to one radiative element, the matrix C being definedwithin one permutation of its rows and/or its columns, Δ being apermutation of the PPM positions of said alphabet, the matrices Ω^((p)),p=1, . . . ,P−1 being a permutation of the PPM modulation positions ofthe (p+1)th sub-alphabet.
 8. Space-time coding method according to claim7, characterised in that at least one matrix Ω^((p)), p=1, . . . ,P−1 isa circular permutation of the PPM modulation positions of the (p+1)thsub-alphabet.
 9. Space-time coding method according to claim 8,characterised in that at least one matrix Ω^((p)), p=1, . . . ,P−1 is acircular shift of the PPM modulation positions of the (p+1)thsub-alphabet.
 10. Coding method according to one of the previous claims,characterised in that the matrix Δ is a circular permutation of saidalphabet.
 11. Space-time coding method according to claim 10,characterised in that the matrix Δ is a circular shift of said alphabet.12. Space-time method according to one of the previous claims,characterised in that the radiative elements are UWB antennas. 13.Transmission method according to one of claims 1 to 11, characterised inthat the radiative elements are laser diodes or light emitting diodes.14. Method according to one of the previous claims, characterised inthat said pulse signal may be a TH-UWB signal.